One of the biggest complaints about Jobseekers' is that it can sometimes be more lucrative to stay on benefits than to take part-time work. By allowing job seekers to take some part-time work, they can get valuable work experience and a 'foot in the door' with an employer, who could eventually hire them permanently.
Furthermore, it would allow a job seeker to do piecemeal work or temporary occasional jobs without fear of losing their benefits. Also, it would eliminate a major source of benefits fraud, by making it no longer fraudulent to work while on jobseekers.
Finally, it would reduce payouts from the benefit system as earnings over the threshold are deducted from benefits payments.